Problem: Reduce to lowest terms: $- \dfrac{5}{6} \div - \dfrac{1}{2} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{1}{2}$ is $- \dfrac{2}{1}$ Therefore: $ - \dfrac{5}{6} \div - \dfrac{1}{2} = - \dfrac{5}{6} \times - \dfrac{2}{1} $ $ \phantom{- \dfrac{5}{6} \times - \dfrac{2}{1}} = \dfrac{-5 \times -2}{6 \times 1} $ $ \phantom{- \dfrac{5}{6} \times - \dfrac{2}{1}} = \dfrac{10}{6} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{10}{6} = \dfrac{10 \div 2}{6 \div 2} = \dfrac{5}{3} $